Abstract
Abstract
Let Habe a-gon with unit edges. DivideHa
into b parts:H
a(1), H
a(2), …, H
a(b) and let the division as Δ(a, b). Let dH
a(k) be the diameter of H
a(k),D(a,b)=max{dH
a(k)}1≤k≤b
, ρ(a, b)=infΔ(a, b){D(a,b)}. We use geometric extremum theory to estimate the range of ρ(a, b), and give the result that ρ(a, b)≥[a(b π)−1 cot(π a
−1)]1/2. For any ε >0, there is a b∈N
+, such that ρ(a, b)< [(2 π (27)−1/2+ ε)a(b π)−1cot(π a
−1)]1/2. We also prove that [6(31/2
π
−1)]1/2≤lim
b→∞
b
1/2
ρ(a, b)≤2.
Subject
Computer Science Applications,History,Education
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